The sheet music is HERE.

Title: McFadden's Trotting Mare. A Fast Ditty.
Composer, Lyricist, Arranger: Words by Phil Rossiter. Music by H. Forest Smith, Jr.
H. Forest Smith, Jr. Publication: Cincinnati: Geo. D. Newhall Co., 56 W. Fourth St., 1885.
Form of Composition: strophic with chorus
Instrumentation: piano and voice
First Line: McFadden was a sporting man, a horse was his delight
First Line of Chorus: The mare was blind in both her eyes, her nose was off the track
Performer: Sung by the Kernells
Dedicatee: Dedicated to the Kernells
Plate Number: 628-3
Subject: Horse racing
Subject: Jockeys
Subject: Accidents
Subject: Gambling
Call No.: Box: 028 Item: 094

The music is also at Music for the Nation: American Sheet Music, 1870-1885 (American Memory, Library of Congress).

~Masato